ATHENS, Feb 1 (Reuters) - Greece's ultra-right Golden Dawn will find a way to contest local and European elections in May despite a crackdown on the party, a senior lawmaker told a defiant crowd of a few thousand supporters in central Athens.

Golden Dawn's leader and five other lawmakers are in jail due to an investigation into whether it is a criminal organization, but it remains Greece's third most popular party.

The fate of the party is being closely watched ahead of the May vote - where it is expected to perform strongly due to a wave of anger against government cuts - amid speculation of new efforts to rein in the group, which denies it is neo-Nazi.

"We will participate in the elections, one way or another," Ilias Kasidiaris, the most prominent public face of the party since its leader's arrest, told about 3,000 supporters rallying in Athens to mark the anniversary of a 1996 dispute over an islet that brought Greece and Turkey to the brink of war.

Two opinion polls published last week showed the party, which has a Swastika-like emblem and believes in ridding Greece of the "stench" of immigrants, would get 8.9 to 10.3 percent of the vote if elections were held now.

Kasidiaris, who plans to run for Athens mayor in May, suggested that a new party, National Dawn, could replace Golden Dawn if it was prevented from running in the election.

"Greek nationalists who have not been involved in criminal organisations, who have no criminal record have founded a new patriotic party, the National Dawn," Kasidiaris said in a sarcastic reference to accusations against the party.

"They put us in jail. And what happened? Did we falter? No, we did not," he said. "We are stronger, we are more powerful and in a short time we will be in power."

Black-clad supporters waved Greek flags and unfurled a banner with the face of leader Nikolaos Mihaloliakos and chanted "traitors" against the government. Some handed out leaflets advertising National Dawn.

Golden Dawn entered parliament for the first time in 2012, tapping resentment against illegal immigrants and politicians blamed for a crisis that has forced thousands out of work and plunged the economy into a six-year recession.

Six of the party's 18 lawmakers including Mihaloliakos are in pre-trial detention over a probe into Golden Dawn and a string of attacks against immigrants and political opponents.

The arrests followed the stabbing of an anti-racist rapper in September by a Golden Dawn sympathiser. The government has resisted calls to ban Golden Dawn, which would be difficult since it would require amending the constitution. (Reporting by Phoebe Fronista and Renee Maltezou; Editing by Deepa Babington and Robin Pomeroy)